Circle
A circle is defined as the set of all points in a plane that are a given distance from a fixed point in the plane. The fixed point is referred to as the center of the circle. The fixed distance, which is the distance from the center of the circle to any point on the rim of the circle, is called the radius. The center of the circle is considered a point of symmetry. Any line through it is called a line a symmetry. A circle has infinite lines of symmetry and one point of symmetry. Circles that have the same center, but not the same radius are called concentric circles.
The circle belongs to the group of curves known as conic sections. The circle can be shown as the intersection of a plane that is perpendicular to the axis of the cone and a right circular cone.
The equation of a circle is (x - h)2 + (y - k)2 = r2, where (h,k) is the center and r is the radius. For example, in the circle described by the equation (x - 3)2 + (y + 2)2 = 100, the center is (3,-2) and the radius is 10.
A circle has many different terms associated with it. Any line or line segment that passes through the center of the circle is called a diameter. The fixed distance in the definition, or the radius, is half the length of the diameter. A chord is a segment that touches the circle in two places. It is a straight-line segment. An arc is part of the perimeter of the circle. It is the portion of the perimeter that lies between two points on the circle. A central angle is an angle formed by having its vertex at the center of the circle and its sides the length of the radius of the circle.
A very important symbol associated with the circle is . The value, often rounded to 3.141592, represents the ratio of the circumference of the circle to the diameter of the circle. This symbol is used heavily in the study of physics and trigonometry. The Greek mathematician Archimedes described the value of between 3 1/7 and 3 10/71. There are several very useful formulas associated with circles that utilize in their calculations. The area of a circle, which represents the space inside the circle, is calculated by multiplying times the radius squared. The circumference, which gives the distance around a circle, is found by multiplying by the diameter of the circle.
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